Conic Sections ...

$$Ay^{2} + By + Cx + D = 0, (ABC\neq 0)$$ be the equation of a parabola, then

If the lines $$3x - 4y - 7 = 0$$ and $$2s - 3y - 5 = 0$$ are two diameters of a circle of area $$49\pi$$ square units, the equation of the circle is-

If the locus of the point $$(4t^2 - 1, 8t-2)$$ represents a parabola then the equation of latus rectum is

If $$A(5,-4)$$ and $$B(7,6)$$ are points in a plane, then the set of all points $$P(x,y)$$ in the plane such that $$AP=PB=2:3$$ is

The equation of the circle which passes through the points $$(2, 3)$$ and $$(4. 5)$$ and the centre lies on the straight line $$y - 4x + 3 = 0$$, is

The equation of the circle, which is the mirror image of the circle, $${ x }^{ 2 }+{ y }^{ 2 }-2x=0$$, in the line, $$y=3-x$$ is:

Point $$\left( 0,\lambda  \right) $$ lies in the interior of circle $$x^2+y^2=c^2$$ then

The equation of the parabola with vertex at (0, 0), axis along x-axis and passing through $$\displaystyle \left( \frac{5}{3}, \frac{10}{3} \right)$$ is

If $$b$$ and $$c$$ are the lengths of the segments of any focal chord of a parabola $$y^{2} = 4ax$$, then length of the semi-latus rectum is

Statement-1 : The only circle having radius $$\sqrt {10}$$ and a diameter along line $$2x + y=5$$ is $$x^2 + y^2 - 6x + 2y=0$$.
Statement-2: The line 2x + y=5 is a normal to the circle $$x^2+ y^2 - 6x + 2y =0.$$